Dynamic Quantum-Assisted Co-Design of Control Tuning and Lyapunov Stability Synthesis for Nonlinear Systems

A new paper on arXiv (2605.04296) presents a quantum-assisted co-design framework for nonlinear closed-loop systems, where controller parameters and Lyapunov-stability certificates are redesigned jointly at successive decision epochs. The key innovation is a two-step structure: first, a Black-Hole-based calibration contracts the continuous admissible search region around the current operating point; then, a finite binary representation is built over that region. The objective is encoded as a local quadratic pseudo-Boolean surrogate, forming an Ising-type Hamiltonian suited for quantum optimization. Quantum imaginary time evolution explores the Hamiltonian, and candidate bitstrings are decoded back into continuous parameters before being re-evaluated on the original nonlinear cost and Lyapunov penalties.

This approach unifies performance improvement and stability synthesis in a single online loop, a departure from conventional nonlinear control that tunes gains offline and verifies stability separately. The framework supports different Lyapunov decay specifications via adjustable penalty terms. Experimental validation on first-order nonlinear consensus, second-order nonlinear consensus, and induction-motor drive control demonstrates practical effectiveness. The implementation code is available on GitHub, making the method accessible for further research and real-world control applications.